本文整理汇总了Python中sympy.functions.erf函数的典型用法代码示例。如果您正苦于以下问题：Python erf函数的具体用法？Python erf怎么用？Python erf使用的例子？那么恭喜您, 这里精选的函数代码示例或许可以为您提供帮助。
在下文中一共展示了erf函数的9个代码示例，这些例子默认根据受欢迎程度排序。您可以为喜欢或者感觉有用的代码点赞，您的评价将有助于系统推荐出更棒的Python代码示例。
示例1: test_normal
def test_normal():
Float.store()
Float.setdps(20)
N = Normal(0, 1)
assert N.mean == 0
assert N.variance == 1
assert N.probability(-1, 1) == erf(1/sqrt(2))
assert N.probability(-1, 0) == erf(1/sqrt(2))/2
N = Normal(2, 4)
assert N.mean == 2
assert N.variance == 16
assert N.confidence(1) == (-oo, oo)
assert N.probability(1, 3) == erf(1/sqrt(32))
for p in [0.1, 0.3, 0.7, 0.9, 0.995]:
a, b = N.confidence(p)
assert operator.abs(float(N.probability(a, b).evalf()) - p) < 1e-10
Float.revert()示例2: test_C99CodePrinter__precision
def test_C99CodePrinter__precision():
n = symbols('n', integer=True)
f32_printer = C99CodePrinter(dict(type_aliases={real: float32}))
f64_printer = C99CodePrinter(dict(type_aliases={real: float64}))
f80_printer = C99CodePrinter(dict(type_aliases={real: float80}))
assert f32_printer.doprint(sin(x+2.1)) == 'sinf(x + 2.1F)'
assert f64_printer.doprint(sin(x+2.1)) == 'sin(x + 2.1000000000000001)'
assert f80_printer.doprint(sin(x+Float('2.0'))) == 'sinl(x + 2.0L)'
for printer, suffix in zip([f32_printer, f64_printer, f80_printer], ['f', '', 'l']):
def check(expr, ref):
assert printer.doprint(expr) == ref.format(s=suffix, S=suffix.upper())
check(Abs(n), 'abs(n)')
check(Abs(x + 2.0), 'fabs{s}(x + 2.0{S})')
check(sin(x + 4.0)**cos(x - 2.0), 'pow{s}(sin{s}(x + 4.0{S}), cos{s}(x - 2.0{S}))')
check(exp(x*8.0), 'exp{s}(8.0{S}*x)')
check(exp2(x), 'exp2{s}(x)')
check(expm1(x*4.0), 'expm1{s}(4.0{S}*x)')
check(Mod(n, 2), '((n) % (2))')
check(Mod(2*n + 3, 3*n + 5), '((2*n + 3) % (3*n + 5))')
check(Mod(x + 2.0, 3.0), 'fmod{s}(1.0{S}*x + 2.0{S}, 3.0{S})')
check(Mod(x, 2.0*x + 3.0), 'fmod{s}(1.0{S}*x, 2.0{S}*x + 3.0{S})')
check(log(x/2), 'log{s}((1.0{S}/2.0{S})*x)')
check(log10(3*x/2), 'log10{s}((3.0{S}/2.0{S})*x)')
check(log2(x*8.0), 'log2{s}(8.0{S}*x)')
check(log1p(x), 'log1p{s}(x)')
check(2**x, 'pow{s}(2, x)')
check(2.0**x, 'pow{s}(2.0{S}, x)')
check(x**3, 'pow{s}(x, 3)')
check(x**4.0, 'pow{s}(x, 4.0{S})')
check(sqrt(3+x), 'sqrt{s}(x + 3)')
check(Cbrt(x-2.0), 'cbrt{s}(x - 2.0{S})')
check(hypot(x, y), 'hypot{s}(x, y)')
check(sin(3.*x + 2.), 'sin{s}(3.0{S}*x + 2.0{S})')
check(cos(3.*x - 1.), 'cos{s}(3.0{S}*x - 1.0{S})')
check(tan(4.*y + 2.), 'tan{s}(4.0{S}*y + 2.0{S})')
check(asin(3.*x + 2.), 'asin{s}(3.0{S}*x + 2.0{S})')
check(acos(3.*x + 2.), 'acos{s}(3.0{S}*x + 2.0{S})')
check(atan(3.*x + 2.), 'atan{s}(3.0{S}*x + 2.0{S})')
check(atan2(3.*x, 2.*y), 'atan2{s}(3.0{S}*x, 2.0{S}*y)')
check(sinh(3.*x + 2.), 'sinh{s}(3.0{S}*x + 2.0{S})')
check(cosh(3.*x - 1.), 'cosh{s}(3.0{S}*x - 1.0{S})')
check(tanh(4.0*y + 2.), 'tanh{s}(4.0{S}*y + 2.0{S})')
check(asinh(3.*x + 2.), 'asinh{s}(3.0{S}*x + 2.0{S})')
check(acosh(3.*x + 2.), 'acosh{s}(3.0{S}*x + 2.0{S})')
check(atanh(3.*x + 2.), 'atanh{s}(3.0{S}*x + 2.0{S})')
check(erf(42.*x), 'erf{s}(42.0{S}*x)')
check(erfc(42.*x), 'erfc{s}(42.0{S}*x)')
check(gamma(x), 'tgamma{s}(x)')
check(loggamma(x), 'lgamma{s}(x)')
check(ceiling(x + 2.), "ceil{s}(x + 2.0{S})")
check(floor(x + 2.), "floor{s}(x + 2.0{S})")
check(fma(x, y, -z), 'fma{s}(x, y, -z)')
check(Max(x, 8.0, x**4.0), 'fmax{s}(8.0{S}, fmax{s}(x, pow{s}(x, 4.0{S})))')
check(Min(x, 2.0), 'fmin{s}(2.0{S}, x)')示例3: test_normal
def test_normal():
dps, mp.dps = mp.dps, 20
N = Normal(0, 1)
assert N.mean == 0
assert N.variance == 1
assert N.probability(-1, 1) == erf(1/sqrt(2))
assert N.probability(-1, 0) == erf(1/sqrt(2))/2
N = Normal(2, 4)
assert N.mean == 2
assert N.variance == 16
assert N.confidence(1) == (-oo, oo)
assert N.probability(1, 3) == erf(1/sqrt(32))
assert N.pdf(1).evalf() == (exp(Rational(-1,32)) / (4*sqrt(2*pi))).evalf()
for p in [0.1, 0.3, 0.7, 0.9, 0.995]:
a, b = N.confidence(p)
assert operator.abs(float(N.probability(a, b).evalf()) - p) < 1e-10
N = Normal(0, 2/sqrt(2*pi))
assert N.pdf(0) == Rational(1,2)
mp.dps = dps示例4: cdf
def cdf(s, x):
"""
Return the cumulative density function as an expression in x
Examples
========
>>> from sympy.statistics import Normal
>>> Normal(1, 2).cdf(0)
-erf(sqrt(2)/4)/2 + 1/2
>>> from sympy.abc import x
>>> Normal(1, 2).cdf(x)
erf(sqrt(2)*(x - 1)/4)/2 + 1/2
"""
x = sympify(x)
return (1+erf((x-s.mu)/(s.sigma*sqrt(2))))/2示例5: confidence
def confidence(s, p):
"""Return a symmetric (p*100)% confidence interval. For example,
p=0.95 gives a 95% confidence interval. Currently this function
only handles numerical values except in the trivial case p=1.
Examples usage:
# One standard deviation
>>> N = Normal(0, 1)
>>> N.confidence(0.68)
(-0.994457883209753, 0.994457883209753)
>>> N.probability(*_).evalf()
0.680000000000000
# Two standard deviations
>>> N = Normal(0, 1)
>>> N.confidence(0.95)
(-1.95996398454005, 1.95996398454005)
>>> N.probability(*_).evalf()
0.950000000000000
"""
if p == 1:
return (-oo, oo)
assert p <= 1
# In terms of n*sigma, we have n = sqrt(2)*ierf(p). The inverse
# error function is not yet implemented in SymPy but can easily be
# computed numerically
from sympy.mpmath import mpf, erf
from sympy.mpmath.calculus import secant
p = mpf(p)
# calculate y = ierf(p) by solving erf(y) - p = 0
y = secant(lambda y: erf(y) - p, 0)
t = Real(str(mpf(float(s.sigma)) * mpf(2)**0.5 * y))
mu = s.mu.evalf()
return (mu-t, mu+t)示例6: heurisch
#.........这里部分代码省略.........
for candidates, rule in rewritables.items():
f = f.rewrite(candidates, rule)
else:
for candidates in rewritables.keys():
if f.has(*candidates):
break
else:
rewrite = True
terms = components(f, x)
if hints is not None:
if not hints:
a = Wild('a', exclude=[x])
b = Wild('b', exclude=[x])
c = Wild('c', exclude=[x])
for g in set(terms):
if g.is_Function:
if g.func is li:
M = g.args[0].match(a*x**b)
if M is not None:
terms.add( x*(li(M[a]*x**M[b]) - (M[a]*x**M[b])**(-1/M[b])*Ei((M[b]+1)*log(M[a]*x**M[b])/M[b])) )
#terms.add( x*(li(M[a]*x**M[b]) - (x**M[b])**(-1/M[b])*Ei((M[b]+1)*log(M[a]*x**M[b])/M[b])) )
#terms.add( x*(li(M[a]*x**M[b]) - x*Ei((M[b]+1)*log(M[a]*x**M[b])/M[b])) )
#terms.add( li(M[a]*x**M[b]) - Ei((M[b]+1)*log(M[a]*x**M[b])/M[b]) )
elif g.func is exp:
M = g.args[0].match(a*x**2)
if M is not None:
if M[a].is_positive:
terms.add(erfi(sqrt(M[a])*x))
else: # M[a].is_negative or unknown
terms.add(erf(sqrt(-M[a])*x))
M = g.args[0].match(a*x**2 + b*x + c)
if M is not None:
if M[a].is_positive:
terms.add(sqrt(pi/4*(-M[a]))*exp(M[c] - M[b]**2/(4*M[a]))*
erfi(sqrt(M[a])*x + M[b]/(2*sqrt(M[a]))))
elif M[a].is_negative:
terms.add(sqrt(pi/4*(-M[a]))*exp(M[c] - M[b]**2/(4*M[a]))*
erf(sqrt(-M[a])*x - M[b]/(2*sqrt(-M[a]))))
M = g.args[0].match(a*log(x)**2)
if M is not None:
if M[a].is_positive:
terms.add(erfi(sqrt(M[a])*log(x) + 1/(2*sqrt(M[a]))))
if M[a].is_negative:
terms.add(erf(sqrt(-M[a])*log(x) - 1/(2*sqrt(-M[a]))))
elif g.is_Pow:
if g.exp.is_Rational and g.exp.q == 2:
M = g.base.match(a*x**2 + b)
if M is not None and M[b].is_positive:
if M[a].is_positive:
terms.add(asinh(sqrt(M[a]/M[b])*x))
elif M[a].is_negative:
terms.add(asin(sqrt(-M[a]/M[b])*x))
M = g.base.match(a*x**2 - b)示例7: heurisch
#.........这里部分代码省略.........
rewritables = {
(sin, cos, cot) : tan,
(sinh, cosh, coth) : tanh,
}
rewrite = kwargs.pop('rewrite', False)
if rewrite:
for candidates, rule in rewritables.iteritems():
f = f.rewrite(candidates, rule)
else:
for candidates in rewritables.iterkeys():
if f.has(*candidates):
break
else:
rewrite = True
terms = components(f, x)
hints = kwargs.get('hints', None)
if hints is not None:
if not hints:
a = Wild('a', exclude=[x])
b = Wild('b', exclude=[x])
for g in set(terms):
if g.is_Function:
if g.func is exp:
M = g.args[0].match(a*x**2)
if M is not None:
terms.add(erf(sqrt(-M[a])*x))
M = g.args[0].match(a*log(x)**2)
if M is not None:
if M[a].is_positive:
terms.add(-I*erf(I*(sqrt(M[a])*log(x)+1/(2*sqrt(M[a])))))
if M[a].is_negative:
terms.add(erf(sqrt(-M[a])*log(x)-1/(2*sqrt(-M[a]))))
elif g.is_Pow:
if g.exp.is_Rational and g.exp.q == 2:
M = g.base.match(a*x**2 + b)
if M is not None and M[b].is_positive:
if M[a].is_positive:
terms.add(asinh(sqrt(M[a]/M[b])*x))
elif M[a].is_negative:
terms.add(asin(sqrt(-M[a]/M[b])*x))
M = g.base.match(a*x**2 - b)
if M is not None and M[b].is_positive:
if M[a].is_positive:
terms.add(acosh(sqrt(M[a]/M[b])*x))
elif M[a].is_negative:
terms.add((-M[b]/2*sqrt(-M[a])*\
atan(sqrt(-M[a])*x/sqrt(M[a]*x**2-M[b]))))
else:
terms |= set(hints)
for g in set(terms):示例8: test_functions_special
def test_functions_special():
assert oclcode(erf(x)) == "erf(x)"
assert oclcode(erfc(x)) == "erfc(x)"
assert oclcode(gamma(x)) == "tgamma(x)"
assert oclcode(loggamma(x)) == "lgamma(x)"示例9: cdf
def cdf(s, x):
"""Return the cumulative density function as an expression in x"""
x = Basic.sympify(x)
return (1+erf((x-s.mu)/(s.sigma*sqrt(2))))/2